We want to find the greatest common factor (GCF) of the terms in the given expression. To do so, we will consider coefficients and variables separately.
21 b- 15 a
Let's start by finding the GCF of 21 and 15.
Factors of21:& 1, 3,7and21
Factors of15:& 1, 3,5and 15
We found that the GCF of the coefficients is 3. To find the GCF of the variables, we need to identify the variables repeated in both terms, and write them with their minimum exponents.
\begin{aligned}
\textbf{Factors of }\bm{1^\text{st}}\textbf{ Variable:}&\ b\\
\textbf{Factors of }\bm{2^\text{nd}}\textbf{ Variable:}&\ a
\end{aligned}
We see that there are not any repeated variable factors.
Thus, the GCF of the expression is 3. Now we can write the given expression in terms of the GCF.
21b-15a ⇔ 3* 7b- 3* 5a
Finally, we will factor out the GCF.
3* 7b- 3* 5a ⇔ 3(7b-5a)
Checking Our Answer
Check your answer âś“
To check our answer, we can apply the Distributive Property and compare the result with the given expression.
